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Topics in portfolio optimisation and systemic risk

Dubois, Mathieu (2015) Topics in portfolio optimisation and systemic risk. PhD thesis, London School of Economics and Political Science.

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This thesis is concerned with different sources of risk occurring in financial markets. We follow a bottom-up approach by carrying out an analysis from the perspective of a single investor to the whole banking system. We first consider an investor who faces parameter uncertainty in a continuous-time financial market. We model the investor’s preference by a power utility function leading to constant relative risk aversion. We show that the loss in expected utility is large when using a simple plug-in strategy for unknown parameters. We also provide theoretical results that show the tradeoff between holding a well-diversified portfolio and a portfolio that is robust against estimation errors. To reduce the effect of estimation, we constrain the weights of the risky assets with a norm leading to a sparse portfolio. We provide analytical results that show how the sparsity of the constrained portfolio depends on the coefficient of relative risk aversion. Based on a simulation study, we demonstrate the existence and the uniqueness of an optimal bound on the norm for each level of relative risk aversion. Next, we consider the interbank lending market as a network in which the nodes represent banks and the directed edges represent interbank liabilities. The interbank network is characterised by the matrix of liabilities whose entries are not directly observable, as bank balance sheets provide only total exposures to the interbank market. Using a Bayesian approach, we assume that each entry follows a Gamma distributed prior. We then construct a Gibbs sampler of the conditional joint distribution of interbank liabilities given total interbank liabilities and total interbank assets. We illustrate our methodology with a stress test on two networks of eleven and seventysix banks. We identify under which circumstances the choice of the prior influences the stability and the structure of the network.

Item Type: Thesis (PhD)
Additional Information: © 2015 Mathieu Steve Dubois
Library of Congress subject classification: H Social Sciences > HG Finance
Sets: Departments > Mathematics
Supervisor: Veraart, Luitgard A. M.

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